Bianchi Type—IX Barotropic Fluid Model with Time-Dependent Displacement Vector in Lyra Geometry

Raj Bali,Rajendra Vadhwani,Jagdish Prasad Dhanka

doi:10.5402/2012/251460

Abstract

Bianchi Type IX barotropic fluid cosmological model in the frame work of Lyra geometry is investigated. To get the deterministic model of the universe, it is assumed that shear () is proportional to expansion (). This leads to , where and are metric potentials and is a constant. To get the results in terms of cosmic time , we have also considered a special case (dust filled universe) and . We find that the model starts with a big bang initially and the displacement vector () is initially large but decreases due to lapse of time. The models and have point-type singularity at and , respectively. The physical and geometrical aspects of the models are also discussed.

Highlights

Bianchi Type IX space-time is the generalization of FRW model with positive curvature
We find that the model starts with a big bang initially and the displacement vector β is initially large but decreases due to lapse of time
We have investigated Bianchi Type IX barotropic fluid cosmological model in the frame work of Lyra geometry

Summary

Introduction

Bianchi Type IX space-time is the generalization of FRW model with positive curvature. Lyra modified Riemannian geometry by introducing a gauge function into the structureless manifold This step removed the main obstackle of Weyl’s theory 10 and made length of vector integrable under parallel displacement. Halford pointed out that constant displacement vector φμ in Lyra geometry plays the role of cosmological constant in General Relativity. P. Singh , Rahman and Bera , Rahman et al , Pradhan et al 17–19 , Bali and Chandnani 20, , Ram et al , and Bali et al , have investigated cosmological models for different Bianchi space time under different contexts in the frame work of Lyra geometry. We have investigated Bianchi Type IX barotropic fluid cosmological model in the frame work of Lyra geometry. The physical and geometrical aspects of the models are discussed

The Metric and Field Equations

Solution of Field Equations

Discussion